The Macroeconomics e¤ects of a Negative Income Tax Martin Lopez-Daneri Department of Economics The University of Iowa February 17, 2010 Abstract I study a revenue neutral tax reform from the actual US Income Tax to a Negative Income Tax (N.I.T.) in a life-cycle economy with individual heterogeneity. I compare di¤erent transfers in a stationary equilibrium. I …nd that the optimal tax rate is 19.51% with a transfer of 11% of GDP per capita, roughly $5,172.79. The average welfare gain amounts to a 1.7% annual increase of individual consumption. All agents bene…t from the reform. There is a 17.52% increase in GDP per capita and a decrease of 13% in Capital per labor. Capital per Output declines 10.22%. 1 Introduction The actual US Income Tax has managed to become increasingly complex, because of its numerous tax credits, deductions, overlapping provisions and increasing marginal rates. The Income Tax introduces a considerable number of distortions in the economy. There have been several proposals to simplify it. However, this paper focuses on one of them: a Negative Income Tax (NIT). In this paper, I ask the following questions: What are the macroeconomic e¤ects of replacing the Income Tax with a Negative Income Tax? Speci…cally, is there any welfare gain from this Revenue-Neutral Reform? Particularly, I am considering a NIT that taxes all income at the same marginal rate and 1 makes a lump-sum transfer to all households. Not only does the tax proposed is simple but also all households have a minimum income assured. In order to answer these questions, I calibrate a life-cycle economy, with heterogeneous agents and endogenous labor supply decisions, to match cer- tain features of the US economy, in the spirit of Imrohoroglu, Imrohoroglu, and Joines (1995), Huggett and Ventura (1999), Imrohoroglu (1989) and Huggett (1996), among others. I consider as a measure of welfare the ex-ante lifetime utility of a newborn in a stationary equilibrium. First, I …nd that replacing the Income Tax by a proportional tax implies a welfare gain equal to an increase in individual consumption of 1:3% per year. The welfare gain is not positive for all types: agents with low productivity are actually worse o¤. There is an increase in the hours worked and the labor supply by 28.78% and 25.4% respectively. There is a positive impact on capital accumulation. For example, Capital over output jumps from 2:7 to 2:74: Consumption is 29:18% higher and keeping …xed leisure in its previous levels gives a welfare gain equivalent to an increase in individual consumption equal to 4:9% per year. Highly productive agents are facing a lower income tax rate. Their income is taxed at a marginal rate of 6:49%: Second, the optimal transfer is 11:02% of the GDP per capita, roughly an annual transfer of $5; 172:79; and a tax rate of 19:51%. Therefore, a house- hold earning $30; 000 a year pays $680:21 in taxes instead of the $979:5 that actually pays with the current Income Tax. In the optimal case, all types of agents favor the reform and the welfare gain equals an annual increase of individual consumption of 1:7% as a result of the better distribution of resources. Hence, the share of consumption of the low productivity agents in- creases 16% from 22:95% to 26:59% and total consumption increases 22:48%. Thus, highly productive agents favor lower levels of transfers. Third, GDP per capita increases by 17:52% and capital per labor de- creases 13%. Higher levels of transfer are related to lower levels of GDP per capita and capital accumulation. Hence, Capital per Output decreases to 2:42. Higher the transfer, higher the proportion of productive agents in the labor supply. Fourth, agents pay taxes when they are working, increasing their tax liabilities when they are more productive in the life-cycle. The net transfer is positive for all agents when they are retired. Also, the proposed tax system is progressive and median productivity agents favor the reform as they were 2 positioned in the kinks of the income bracket and the new tax allows them to smooth consumption more e¢ ciently. Finally, all agents consume more at all ages with the tax reform. 1.1 Related literature Juliet Rhys-Williams and Milton Friedman (1962) were the …rst to develop the concept of a Negative Income tax. Despite of its popularity in the seven- ties and a failed attempt to introduce it as legislation during Richard Nixon’s Presidency, a study of the Negative Income Tax in a general equilibrium set- ting has been largely neglected due to the computational limitations of the time. Nevertheless, the number of studies in the subject is considerable; see Mo¢ t (2003) and Meltzer (2003) for example. This paper is part of the literature on optimal taxation (see Mirrlees (1971) and Stern (1976)) and follows a quantitative approach in the same lines as in Ventura (1999), Domeij and Heathcote (2004), Conesa and Krueger (2006) and Conesa, Kitao, and Krueger (2009), among others. Ventura (1999) studies the quantitative general equilibrium implications of a Flat Tax Reform and …nds a positive impact in capital accumulation and labor supply, and a higher concentration of earnings and wealth. Domeij and Heathcote (2004) study the e¤ects of reducing capital taxes in two settings: a repre- sentative agent and a standard incomplete market model and conclude that the welfare gains of reducing capital taxes are bigger in the former. Conesa and Krueger (2006) analyze the optimal progressivity of the income tax code and …nd that a ‡at tax rate of 17:2% and a deduction of $9; 400 are optimal for the US, with a welfare gain of 1:7% in indivdual consumption: Conesa, Kitao, and Krueger (2009) allow a distinction between capital and labor in- come and conclude that in the US, the optimal income tax rate is 36% and a labor tax rate of 23% with a deduction of $7; 200. The paper proceeds as follows: Section 2 describes the model and de…nes the equilibrium, Section 3 explains the calibration, Section 4 presents the results and Section 5 concludes. 3 2 The model 2.1 General Framework I study a general equilibrium life-cycle economy consisting of D overlapping generations. Agents are heterogeneous and face no idiosyncratic risk. There is neither life nor aggregate uncertainty. Time is discrete. Agents value consumption and leisure. Every period, given competitive prices, they decide how much to consume, save and work. There is an ex- ogenously retirement age and a one-period risk-free asset. Neither borrowing nor short selling is allowed. Heterogeneity arises from two factors: age and type. A newborn faces a given probability of belonging to one of M di¤erent types. Each of them has its own inborn productivity, which is kept constant for the rest of the agent’s life1. Age also plays a role in productivity. On the other hand, for every type, the agent’se¢ ciency pro…le evolves through time. Therefore, it is not going to be the same the work in e¢ ciency units supplied to the market by a young, a middle-age and an old agent. There is a government that collects taxes and runs a balanced budget. In the following paragraphs, I will give a formal description of the model. 2.2 Demographics A continuum of agents is born at each date. The size of the newborns is normalized to be equal to one. The mass population at time t is given by Nt and evolves through time at a growth rate n. All agents live D periods. The …rst R periods of their life, agents are involved in productive activities and in the following D R, they are retired. The age R is exogenous. The demographic structure is stationary. Therefore, at any given point in time, the fraction j of age j individuals in the population is constant. 1 This feature of the model contemplates the fact that agents di¤er themselves through innate abilities or, for instance, their levels of education. 4 2.3 Endowment, Preferences and Labor Productivity Agents are born with zero assets. At every period of their working life, they are endowed with one unit of time that they supply to the market at a competitive wage rate All agents share the same preferences over streams of leisure and con- sumption given by the time-separable utility function: D j u (cj;t; 1 lj;t) j=1 X where cj;t and lj;t stands for consumption and leisure at age j J = 2 1;:::;D and period t; respectively: The momentary utility function be- longsf to theg Constant Relative Risk Aversion (CRRA) class and is given by: 1 1 c (1 l) 1 These preferences display a unitary intratemporal elasticity of substitu- tion. Consumption and leisure are not separable. The parameter (0; 1) shapes the time spent working and in‡uences the degree of risk of2 aver- sion2 and the Frisch elasticity of labor supply. The latter gives the elasticity of hours worked to changes in wages, keeping the marginal productivity of consumption constant. The Frisch elasticity is: (1 l) [1 (1 )] (; ; l) = l At the beginning of her life, an agent face a probability pi > 0 of belonging to one of M particular ability types i I = 1;:::;M . The type i together with the age j determine the agent’s2 productivityf e (gi; j) E. Therefore, her productivity is divided into a …xed component given by2 her type, and a variable one represented by her age.